Ike would not recognize, nor side with today’s Democrat Party... it would repulse him. Ike was a man of honor and principle... two qualities alien to modern Democrats.
His cabinet was composed of several big businessmen and one union leader, often referred to as "eight millionaires and a plumber." He appointed several conservative judges, but also Earl Warren and William Brennan. In his defense, he later called those appointments the worst mistake of his presidency.
I think as conservatives we tend to think of previous generations being conservative. Although they were sexually, in terms of massive government programs the WWII generation was right up there.